[GAP Forum] presentations of Lie algebras in GAP

[Willem de Graaf]

Dear Forum, Jianrong,

Currently there is no functionality in GAP for the problem that
you describe (getting a presentation of a given Lie algebra).
However, if the Lie algebra is finite dimensional one can take
as generators the elements of a basis, and the relations follow
from the multiplication table. It would, however, not be a very
interesting presentation.

Best wishes,

Willem de Graaf

On Tue, Dec 18, 2012 at 1:30 AM, Jianrong Li <lijr07 at gmail.com> wrote:
> Dear Forum,
>
> If we know a set of generator of a Lie algebra, can we use GAP to give a
> presentation of the Lie algebra? For example, for $sl_2$ (over
> $\mathbb{C}$), if we know $e=(0, 1; 0, 0)$, $f=(0, 0; 1, 0)$ , $h=(1, 0; 0,
> -1)$, how to write a presentation of $sl_2$ from these matrices?
>
> What about the case of positive characteristics ($\mathbb{C}$ is replaced
> by some field of a positive characteristic)?
>
> Thank you very much.
> With best wishes,
> Jianrong.
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